You can take the Greyhound bus which offers Web fares in advance. You would need to take a taxi from the airport to the bus station as they are on opposite ends of town. According to Greyhound site, it would be a lengthy journey--about 5-7 hours depending on which bus you caught. You also have to get off bus at border and go through immigration/security. This may be your cheapest way as I could find a round trip for $72 for October on the Web Fare. Not sure what taxi would cost each way--maybe $15-20? Unfortunately we don't have city bus service to the airport.
There is a Canadian airport bus service, called Quick Shuttle, that runs from the Bellingham airport 5-8 times a day depending on the season. This shuttle will only take you as far as Vancouver airport or downtown however. It does go to Vancouver Airport where you could get Pacific Coach Line bus to Whistler. I think this will be more expensive though.
There is a scenic train service from Vancouver to Whistler but it is very pricey.